One song I learned was Dominic Behan's The Foggy Dew. (i.e. the one about the Easter Rising in 1916). You may disagree with its sentiments, but it is ideal for practicing barre chords. If you play it in C minor, you can do it without using any open chords at all (hint: Cm7 does double duty as an odd-sounding but acceptable E major chord).

I normally play and sing it in Bm, which means that it uses open D and A chords. I find it more difficult to switch from barre to open chords and back again, than to switch between barreed A-, E- and Em shapes.

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